I wasn't going to say "Don't leave reviews just asking for updates", I was planning on saying "Please stop telling me to update, as I am very busy and in grad school", which could potentially come across differently. I've had people who have been messaging me to ask when I was going to update/why I hadn't updated yet who haven't left reviews. I wasn't going to mention reviews at all.

That has the potential to come across as rude. I'd probably stop looking for updates if an author posted something like that. Just make it simple and gracious (as you should be glad they're looking forward to your work ): "I'm in grad school so updates may take some time. Your patience is appreciated!"

I definitely think it would be bad idea to scold people who are reading your work. "Update soon" to me obviously means that they like the story so much they can't wait for your next installment to come out. Why not take it in the spirit it was intedned?

This. "Please update soon!" = "This is so great I can't wait for more!"

I never got into ff.net because it wasn't user-friendly with my older Mac ... so my fanfic is all on LiveJournal, where it's easy to reply to reviews. When I get the "pleeease update soon!" comments, I just reply with something like "Working on next chapter now -- stay tuned," or "Hope to have next chapter up after Christmas/in a week or so/by the weekend."